超指数相互作用模型中的多体效应
Many-Body Effects in Models with Superexponential Interactions
摘要：
超指数系统的特征在于，动力学自由度出现在幂律的底和指数中的势。我们探讨了由超指数势支配的多体系统的散射动力学。每个潜在的长期表现出一个特征交叉通过两个鞍点从一个区域与限制通道的两个区域的渐近自由运动。随着通道中散射能量的增加，我们观察到从直接后向散射行为到该通道中的多个后向散射和散射事件的过渡。我们详细分析了这种转变，探索个人的多体轨迹和大型统计合奏的轨迹的属性。在鞍点以下和鞍点以上的能量发生的振荡轨迹，通常表现出间歇性的振荡行为与强烈变化的振幅。在统计系综的情况下，进入通道的反射时间的分布随着能量的增加而从两个平台结构变化为单个宽的不对称峰结构。这可以通过分析相应的动量-时间图来理解，这些图经历了从二值曲线到宽分布的过渡。最后，我们提供了一个展望这些不寻常的模型系统的未来前景。
英文摘要：
Superexponential systems are characterized by a potential where dynamical degrees of freedom appear in both the base and the exponent of a power law. We explore the scattering dynamics of many-body systems governed by superexponential potentials. Each potential term exhibits a characteristic crossover via two saddle points from a region with a confining channel to two regions of asymptotically free motion. With increasing scattering energy in the channel we observe a transition from a direct backscattering behaviour to multiple backscattering and recollision events in this channel. We analyze this transition in detail by exploring both the properties of individual many-body trajectories and of large statistical ensembles of trajectories. The recollision trajectories occur for energies below and above the saddle points and typically exhibit an intermittent oscillatory behaviour with strongly varying amplitudes. In case of statistical ensembles the distribution of reflection times into the channel changes with increasing energy from a two-plateau structure to a single broad asymmetric peak structure. This can be understood by analyzing the corresponding momentum-time maps which undergo a transition from a two-valued curve to a broad distribution. We close by providing an outlook onto future perspectives of these uncommon model systems.
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